CDMA receiver with parallel interference suppression and with weighting

ABSTRACT

A CDMA receiver with parallel interference suppression and with weighting. The weighting coefficients of the outputs from the various stages of the receiver are chosen in order to minimize a quadratic error weighted by the distribution of the pertinent values of the intercorrelation matrix.

TECHNICAL FIELD

The present invention relates to a CDMA receiver, i.e. a receiver withCode Division Multiple Access. It finds application intelecommunications and notably in mobile radio systems.

STATE OF THE PRIOR ART

The advantages of CDMA communications no longer need to be demonstrated.It is known that this technique consists of spreading a signal by apseudo-random sequence, allocating to each user his own sequence, theallocated sequences being orthogonal to one another, transmitting all ofthe signals thus spread and then, on reception, narrowing down thereceived signal with the help of the sequences used at transmission andfinally reconstituting the signals pertinent to each user.

If the various sequences of the spreading were strictly orthogonal toeach other and if the propagation signals were perfect, the signalspertinent to each user would be reconstituted without any error.However, in reality, things are not so simple and each user interferesto a greater or lesser extent with the others.

In order to reduce these effects, referred to as multiple accessinterference it has been necessary to envisage correction means arrangedin the receiver.

By way of example, one may describe the receiver that is the subject ofU.S. Pat. No. 5,553,062.

FIG. 1 appended substantially reproduces FIG. 1 of the document quoted.The circuit shown allows one to supply a nominal signal designated{circumflex over (d)}₁, belonging to a first user. To do this, it usesan input circuit 41, receiving a signal R(t) from the multipliers 51,61, . . . , 71 connected to the generators of the pseudo-randomsequences (PRS) 52, 62, . . . , 72, which reproduce the sequences usedfor transmission by the various users, delay circuits 53, 63, . . . ,73, amplifiers (AMP) 54, 64, . . . , 74, and multipliers 55, 65, . . . ,75. If one assumes that there are K users, there are K channels of thistype arranged in parallel. The last K−1 channels permit the extractionof K−1 signals pertinent to K−1 channels and then to respread these K−1signals by the corresponding pseudo-random sequences. One can thensubtract from the general input signal R(t) all of these respread K−1signals. To do this, a delay line 48 is provided in order to hold backthe input signal R(t) for the duration of the formation of the respreadK−1 signals, the respread K−1 signals and the delayed input signal beingsubsequently applied to a subtractor 150. This supplies a global signalfrom which the signals belonging to the K−1 users other than the firstone, have been removed. One can then correlate this signal with thepseudo-random sequence belonging to the first user in a multiplier 147,which receives the pseudo-random sequence supplied by the generator 52,a sequence suitably delayed by a delay line 53. An amplifier 146 thensupplies the estimated data {circumflex over (d)}₁, pertinent to thefirst user.

This structure can be repeated K times in order to process the K signalspertinent to the K users. Hence K first estimations of the data{circumflex over (d)}₁, {circumflex over (d)}₂, . . . , {circumflex over(d)}_(k) are obtained.

This procedure can be repeated in a second interference suppressionstage and so on. FIG. 2 appended shows, diagrammatically s stages, thefirst E₀ being, strictly speaking, an ordinary correlation stage, theothers E₁, . . . , E_(i), . . . , E_(s−1) being interference suppressionstages.

One can still further improve the performance of such a receiver byusing, not the last estimation obtained, but a weighted mean of thevarious estimates provided. This amounts to allocating a weight w_(i) tothe estimation {circumflex over (d)}₁, and forming the sum of theW_(i){circumflex over (d)}_(i) signals. In FIG. 2, it can be seen thatall the signals supplied by stage E₀ are multiplied by a coefficient w₀in a multiplier M₀, all the signals supplied by stage E₁ are multipliedby a coefficient w₁ in a multiplier M₁, all the signals supplied bystage E_(i) are multiplied by a coefficient w_(i) in a multiplier M_(i),and all the signals supplied by the final stage E_(s−1) by a coefficientw_(s−1) in a multiplier M_(s−1). An adder ADD then forms the sum of thesignals supplied by the multipliers.

FIG. 2 also allows one to make clear certain notations appropriate tothis technique. At the output of a stage, K signals are to be foundcorresponding to K users. Rather than individually marking these signalsone can consider, in a more synthetic way, that they are the Kcomponents of a “vector”. At the output of stage E_(i) one will find Ksignals which are the K components of a vector designated {overscore(Z)}_(i). At the output of the multipliers M₀, M₁, . . . , M_(i), . . ., M_(s−1), one will therefore find, with this synthetic notation,vectors w₀{overscore (Z)}₀, . . . , w₁{overscore (Z)}₁, . . . ,w_(i){overscore (Z)}_(i), . . . , w_(s−1){overscore (Z)}_(s−1). Theoutput from the adder will therefore be designated {overscore (Z)} andone can write: $\begin{matrix}{\overset{\_}{Z} = {\sum\limits_{i = 0}^{s - 1}{w_{i}{\overset{\_}{Z}}_{i}}}} & (1)\end{matrix}$

There remains the question of determining the weighting coefficients wi.In the document U.S. Pat. No. 5,553,062 already mentioned, an empiricallaw w_(i)=1/2^(i) was proposed (column 12, line 30) without anyjustification. This amounts to weighting the outputs from the stages ina decreasing way.

Furthermore, the article by S. MOSHAVI et al., entitled “MultistageLinear Receivers for DS-CDMA Systems” published in the magazine“International Journal of Wireless Information Networks”, vol. 3, No. 1,1996, pages 1-17, takes up certain ideas from the patent U.S. Pat. No.5,553,062 already mentioned and develops the theory of this type ofreceiver. It also proposes an optimization of the weightingcoefficients.

Without going into the details of this theory, which is complex andwould depart from the context of this invention, one can summarize it inthe following way.

If each user only transmitted a single binary signal (or bit), one wouldfind, in the receiver, signals including, for each user, the bit whichis pertinent to him, to which would be added the parasitic interferencesignals due to the presence of other users. At the output from eachstage, one would find a group of K bits that can be considered as the Kcomponents of a vector. At the output from the following stage, onewould again find K signals and one would be able to characterize thetransfer function of the stage by a matrix of K lines by K columns, thediagonal elements of this matrix would be the autocorrelationcoefficients and the other elements, intercorrelation coefficientsbetween different users.

In practice, however, the transmitted signal does not comprise onesingle bit but N bits, so that the values in question are no longer ofdimension K but of dimension NK. The transfer matrix is then a matrix ofNK lines and NK columns.

If one designates {overscore (d)} the data vector (which has NKcomponents), and the vector at the output from the first decorrelationstage (or matched filtering stage) is designated {overscore (y)}_(mf)(the index mf referring to the matched filtering function), one maywrite, ignoring the noise,

{overscore (y)} _(mf) =R{overscore (d)}

where R is an NK by NK correlation matrix. The matrix R can be brokendown into K by K sub-matrices, all of which are identical if the usersuse the same broadcasting code for all the bits of the total message.However, this is not necessarily so in all cases.

In a precise way, for a bit in row i, the coefficient for line j and forcolumn k of the correlation matrix is of the form:

P _(j.k) (i)=∫_(r) _(j) ^(T) ^(_(b)) ^(−τ) ^(_(j)) α_(j) (t−τ _(j))a_(k)(t−τ _(k) −iT _(b))dt

where a_(j) and a_(k) are the values (+1 or −1) of the pulses (or“chip”) of the pseudo-random sequences, T_(b) is the duration of a bit,τ_(j) and τ_(k) are delays.

Each stage of interference suppression repeats the transformationoperated by the matrix R, so that at the output of stage E₁ one finds asignal R{overscore (y)}_(mf), and at the output from the i^(th) stage, asignal R^(i){overscore (y)}_(mf).

If the weighted sum of the signals supplied is processed by all thestages of the receiver, one obtains an estimation {overscore (d)} of thedata in the form: $\begin{matrix}{\overset{\_}{d} = {\sum\limits_{i = 0}^{s - 1}{w_{i}R^{i}{\overset{\_}{y}}_{mf}}}} & (2)\end{matrix}$

where s is the total number of stages, one being a normal filteringstage and s−1 interference suppression stages.

There are particular detector circuits which, in theory, minimize theerrors committed in the transmission and which are called Minimum MeanSquare Error Detectors or MMSE detectors for short. For these detectors,the matrix for passage between the input and the output is:

[R+N ₀I]⁻¹

where I is a unit matrix of the same rank as R, and N₀ the spectraldensity of noise power. If one wishes to produce a receiver providingperformance close to that of an ideal receiver, the weightingcoefficients w_(i) must be chosen in such a way that the weighted sum isas close as possible to the inverse of the matrix [R+N₀I]:$\begin{matrix}{{\sum\limits_{i = 0}^{s - 1}{w_{i}R^{i}}} \cong \lbrack {R + {N_{0}I}} \rbrack^{- 1}} & (3)\end{matrix}$

The weighted sum is precisely the quantity formed by the circuit in FIG.2.

This relationship between matrices can be transposed into severalequations using values pertinent to the matrices concerned. It is knownthat, for certain conditions, which are in general fulfilled in thedomain in question, one can transform a matrix into a matrix where theonly elements not zero are those of the diagonal, elements which are thevalues that are pertinent to the matrix. Each of the matrices inequation (3) being from row NK, there are in general NK pertinentvalues, that one can designate λ_(j). Each matrix of equation (3) havingbeen thus diagonalized, one obtains NK equations for the pertinent NKvalues. One will seek therefore, for each pertinent value, to make theapproximation: $\begin{matrix}{{\sum\limits_{i = 0}^{s - 1}{w_{i}\lambda_{j}^{i}}} \cong {1/( {\lambda_{j} + N_{0}} )}} & (4)\end{matrix}$

Therefore one is in the presence of a polynomial expansion in λ_(j) ofdegree s−1. For each λ_(j) one obtains an equation in λ_(j) where theunknown is w_(i). If the number of stages s is equal to the number ofpertinent values NK, then one has NK equations with NK unknown values ofw_(i) which one would be able to resolve. However, in practice, thenumber of stages s is very much lower than the number NK so that thenumber of unknowns is very much lower than the number of equations. Onecannot therefore satisfy all these equations simultaneously and one musttherefore be content with an approximation.

The article by S. MOSHAVI et al. already mentioned proposes a particularchoice criterion based on the following considerations. The error madebetween the weighted sum and the reciprocal of λ_(j)+N₀ being designatede_(j), the article suggests that one should not consider this error butits square weighted by a function that depends on the relevant value ofλ_(j) and of the noise N₀ and to minimize the sum of these weightederrors for all the pertinent values. In other words, it is suggestedthat one minimizes the quantity: $\begin{matrix}{\sum\limits_{j = 0}^{{NK} - 1}{{h( {\lambda_{j} \cdot N_{0}} )}e_{j}^{2}}} & (5)\end{matrix}$

where h (λ_(j).N₀) is the weighting function with $\begin{matrix}{e_{j} = {{\sum\limits_{j = 0}^{s - 1}{w_{1}\lambda_{j}^{i}}} - {1/( {\lambda_{j} + N_{0}} )}}} & (6)\end{matrix}$

For various reasons that are explained in the article mentioned, theauthors chose as the weighting function, a quadratic function λ_(j)²+N₀λ_(j), which means that the large pertinent values are favored.

The objective of this invention is to improve this technique by making adifferent choice for the weighting function, the aim being to reducefurther the error made on the transmission of the data.

DESCRIPTION OF THE INVENTION

To this end, the invention recommends using, as the weighting function,the frequency distribution of the relevant values, which will bedesignated p(λ)and which is the function that gives the number ofpertinent values contained in a given interval.

Using the previous notation, this comes down to minimizing the quantity:$\begin{matrix}{\sum\limits_{j = 0}^{{NK} - 1}{{p(\lambda)}\lbrack {{\sum\limits_{j = 0}^{s - 1}{w_{i}\lambda_{j}^{i}}} - \frac{1}{\lambda_{j} + N_{0}}} \rbrack}^{2}} & (7)\end{matrix}$

In a precise way, the subject of this invention is a receiver for CodeDivision Multiple Access transmission through CDMA codes, thistransmission being accessible to a plurality of K users eachtransmitting a message made up of a plurality of N binary data, each setof data pertinent to a user being transmitted after spectrum spreadingby a pseudo-random binary sequence pertinent to this user, this receivercomprising s stages in series, of which

a first reception stage of a global signal corresponding to the whole ofthe signals transmitted by the K users, this first stage comprising Kchannels in parallel, each channel being allocated a particularpseudo-random sequence and being capable of supplying a first estimationof the received data that corresponds to the user, having used thispseudo-random sequence, this first stage thereby supplying K signals onK outputs,

(s−1) multiple access interference suppression stages, each of thesestages having K inputs and K outputs, the K inputs of the firstinterference suppression stage being linked to the K outputs from thefirst reception stage, and the K inputs of the other interferencesuppression stages being linked to the K outputs from the interferencesuppression stage that precedes it,

means of weighting each group of K signals supplied by the K outputs ofeach of the s stages, the output signals of a stage of row i (i beingbetween 0 and s−1) being weighted by a coefficient β_(i), thecoefficients β_(i) being chosen so that a certain quantity should be aminimum,

an adder with s groups of K inputs to receive the s groups of K weightedsignals,

a decision means linked to the adder and receiving, for each user, aweighted sum of signals and supplying the corresponding data finallytransmitted,

this receiver being characterized by the choice of the weightingcoefficients β_(I) being made in the following way:

A being a matrix of NK lines and NK columns in which the elements of themain diagonal are zeros and the elements outside the diagonal reflectthe intercorrelations between the signals transmitted by the K users forthe N different binary data of the messages transmitted, this matrix Ahaving NK pertinent values λ_(j) distributed according to a certaindistribution p(λ),

the polynomial expansion α₀λ⁰ _(j)+α₁λ¹ _(j)+. . . +α_(i)λ^(i) _(j)+. .. +α_(s−1)λ_(j) ^(s−1), where the α_(i) are coefficients, having withthe quantity 1/(1+λ_(j)), a deviation designated e(λ_(j)) for eachpertinent value λ_(j),

the quantity that one makes a minimum is the sum, for all pertinentvalues λ_(j) of the square of this deviation, weighted by thedistribution of the pertinent values, i.e.${\sum\limits_{j = 0}^{{NK} - 1}\quad {p\quad {(\lambda)\lbrack {e( \lambda_{j} )} \rbrack}^{2}}},$

with in addition the condition Σp(λ_(j))e(λ_(j))=0, this doubleconstraint defining the coefficients α_(i),

the weighting coefficients β_(I) modifying each stage of the receiverare derived from coefficients α_(i) by the equationsβ_(i)=(−1)^(i)(α_(i)+α_(i+1)) for values of i going from 0 to s−2 andβ_(i)=(−1)^(i)α_(i) for i=s−1.

Preferably, for distribution p(λ) of the pertinent values for the matrixA, an expression approximately equal to γ²(λ+1−a)exp[−γ(λ+1−a)] where γand a are suitable constants.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1, already described, shows a part of a known receiver;

FIG. 2, already described, illustrates the use of a weighting of outputsfrom the various stages;

FIG. 3 shows some examples of distributions of the pertinent values of amatrix;

FIG. 4 illustrates the theoretical performance of a receiver conformingto the invention, compared to the performance of known receivers;

FIG. 5 permits a comparison to be made between different receivers,under certain using conditions;

FIG. 6 allows another comparison to be made between different receivers

FIG. 7 shows diagrammatically the general structure of a receiveraccording to the invention in the particular case of five users andthree stages;

FIG. 8 shows a flow chart illustrating a general algorithm;

FIG. 9 shows a flow chart applied to the particular case of the circuitin FIG. 7

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

The matrix R used in the matters considered above, can be advantageouslyreplaced by a matrix A, obtained by subtracting from R the unit matrix Ithe only elements of which are the diagonal terms equal to 1:

A=R−I or R=A+I

In effect, in the matrix R one finds not only the coefficientsreflecting the interference between different users for bits of the samerow or of different rows (coefficients outside the diagonal) but alsocorrelation coefficients for one and the same user (coefficients of thediagonal) and these coefficients are all equal to 1. The suppression ofinterference is therefore better linked to a matrix A in which all thediagonal elements are zero, since it only contains terms that expressintercorrelations. This matrix is the matrix A.

The matrices R and A have different traces since the trace of a matrixis equal to the sum of the terms in its diagonal. For the matrix R, thetrace is equal to NK while it is zero for the matrix A. It is known thatthe mean of the values belonging to a matrix is equal to its tracedivided by its row, so that the mean of the values belonging to thematrix R is equal to NK/NK or 1, while the mean of the values belongingto matrix A is zero. The distribution p(λ) of the values belonging tomatrix A is therefore centered on zero.

If {overscore (y)} designates the signals applied to the K inputs of aninterference suppression stage, one finds at the output from thesuppression circuit characterized by the matrix A, a signal Ay, that issubtracted from the incident signal, or Iy so that the output from thisfirst stage is of the form I{overscore (y)}−A{overscore (y)} or(I−A){overscore (y)}.

The second stage again processes the signal (I-A){overscore (y)} throughthe matrix A, which gives (I−A)A{overscore (y)}, which one againsubtracts from I{overscore (y)} to obtain (I−A+A²){overscore (y)} and soon. At the output from the i^(th) stage one therefore finds signals{overscore (Z)}_(i), of the form: $\begin{matrix}{{\overset{\_}{Z}}_{i} = {\sum\limits_{j = 0}^{i}{( {- A} )^{j}\overset{\_}{y}}}} & (8)\end{matrix}$

where the index i runs from 0 to s−1.

If one linearly combines the outputs of these stages using coefficientsthat will be designated β_(i) (with i=0, 1, . . . , s−1) (in order todistinguish them from the coefficients w_(i) of the prior art), oneobtains a signal {overscore (Z)}of the form: $\begin{matrix}{\overset{\_}{Z} = {\sum\limits_{i = 0}^{s - 1}{\beta_{i}{\overset{\_}{Z}}_{i}}}} & (9)\end{matrix}$

or, by replacing Z_(i) by its value taken from (8): $\begin{matrix}{\overset{\_}{Z} = {\sum\limits_{i = 0}^{s - 1}{{\beta_{i}( {\sum\limits_{j = 0}^{i}( {- A} )^{j}} )}{\overset{\_}{Z}}_{0}}}} & (10)\end{matrix}$

The expression (10) is a linear combination of A^(j) with coefficientsthat are designated α_(j): $\begin{matrix}{\overset{\_}{Z} = {( {\sum\limits_{i = 0}^{s - 1}{\alpha_{i}A^{i}}} ){\overset{\_}{Z}}_{0}}} & (11)\end{matrix}$

In order to get closer to an ideal detector with decorrelation, thetransfer function of which would be R⁻¹, i.e. (I+A)⁻¹, one seeks to givethe polynomial expansion (11) a value as close as possible to (I+A)⁻¹or: $\begin{matrix}{{\sum\limits_{i = 0}^{s - 1}{\alpha_{i}A^{i}}} \cong ( {I + A} )^{- 1}} & (12)\end{matrix}$

which can be expressed, in terms of pertinent values λ_(j), by theapproximation: $\begin{matrix}{{\sum\limits_{i = 0}^{s - 1}{\alpha_{i}\lambda_{j}^{i}}} \cong {1/( {1 + \lambda_{j}} )}} & (13)\end{matrix}$

for all NK values of j, or j=0, 1, 2, . . . , (NK−1).

Starting from the chosen coefficients α_(i) one can go back to thecoefficients β_(i) by establishing the equations that link these twotypes of coefficients. In order to find these equations, it suffices toexpand the quantities$\sum\limits_{i}{\beta_{i}{\sum\limits_{j}{( {- A} )^{j}\quad {and}\quad {\sum\limits_{i}{\alpha_{i}A^{i}}}}}}$

and E nd to equalize the coefficients of the same power of A^(i). Onethen finds, for all values of i from i=0 to i=s−2:

β_(i)=(−1)^(i)(α_(i)+α_(i+1))  (14)

and for the last one i=s−1:

β_(s−1)=(−1)^(s−)α_(s−1)  (15)

According to the invention, the coefficients ai are subject to a doubleconstraint, which is, designating e(λ) the difference between 1/(1+λ)and $\sum\limits_{i = 0}^{s - 1}{\alpha_{i}{\lambda^{i}:}}$

$\begin{matrix}{{\sum\limits_{j}{{p( \lambda_{j} )}{e( \lambda_{j} )}}} = 0} & (16) \\{\sum\limits_{i}{{{p(\lambda)}\lbrack {e( \lambda_{j} )} \rbrack}^{2}\quad {minimum}}} & (17)\end{matrix}$

where p(λ) is the distribution of the pertinent values. As the number ofpertinent values is very large, it may be considered that λ is acontinuous variable and that the separate summations are integrals. Theconstraints become:

∫_(R) p(λ)e(λ)dλ=0  (18)

∫_(R) p(λ)[e (λ)]² dλ minimum  (19)

where R is the distribution zone of the pertinent values. The firstexpression (18) expresses that the mean error made is zero, and thesecond (19) the minimum variance of this error.

For synchronous type communications (the values of τ_(i) are equal), thevariance of the pertinent values, i.e. the mean of the sum of thesquares of the deviation of the pertinent values with respect to themean of these pertinent values is given theoretically by:$\begin{matrix}{\sigma_{\lambda}^{2} = \frac{( {K - 1} )}{M}} & (20)\end{matrix}$

where K is the number of users and M is the processing gain, i.e. theratio between the duration of a transmitted bit and the duration of thechips of the pseudo-random sequences (cf. the article by S. MOSHAVIalready mentioned, equation 58). In practice (σ² _(λ) is determined bythe simulation processes. For asynchronous communications (the values ofτ_(i) are different), this variance is estimated by simulationprocesses.

In order to express quantitatively the distribution p(λ) of thepertinent values, preferably one uses an approximation suggested in thework by A. PAPOULI entitled “Probability, Random Variables, andStochastic Processes”, McGraw Hill, Second Edition, 1985. This workgives for such a distribution the following approximation:

p(λ)=γ²(λ+1−a)exp[−γ(λ+1−a)]  (21)

for λ≧α−1, with

γ=1.6785/σ_(λ)

a=1−1.3685 /γ

In order to illustrate this question of the distribution of thepertinent values, FIG. 3 shows some distributions obtained in the caseof pseudo-random sequences of 63 chips for a variable number of users K(K=5, 7, 10, 15) and for synchronous transmissions. One checks on theway that the pertinent values distribute themselves correctly about 0,since their mean is zero.

According to the invention, the equality (16) is provided and thequantity (17) is minimized.

By using the approximation referred to, valid for λ≧α−1 and by takingout the coefficient γ² and, in the exponential, the factor exp(−γ+γa)which does not depend on λ, and by taking an integral form and not adiscreet sum, one obtains the equation:

∫_(α−1) ^(∞)(λ+1−a)exp(−γλ)e(λ)dλ=0  (22)

and the quantity

∫_(α−1) ^(∞)(λ+1−a) exp (−γλ)e² (λ) dλ  (23)

is minimized.

Equation 22 supplies${{\frac{\exp ( {- {\gamma ( {a - 1} )}} )}{\gamma}a\quad \xi} - {\sum\limits_{k - 1}^{s - 1}{a_{k}\lbrack {{v( {k + 1} )} + {( {1 - a} ){v(k)}}} \rbrack}}} = 0$

where:$\xi = {\int_{\alpha - 1}^{+ \infty}{\frac{\exp ( {- {\gamma\lambda}} )}{\lambda + 1}{\lambda}}}$

which works out numerically:${v(k)} = {{{{\exp ( {- {\gamma ( {a - 1} )}} )}{\sum\limits_{n = 0}^{k = 1}{\frac{k!}{( {n - n} )!}\frac{( {a - 1} )^{k - n}}{\gamma^{n + 1}}}}} + {\frac{k!}{\gamma^{k + 1}}\quad {for}\quad k}} \neq 0}$${{{v(k)}\frac{k}{\gamma}{v( {k - 1} )}} + {\frac{( {a - 1} )^{k}}{\gamma}{\exp ( {- {\gamma ( {a - 1} )}} )}}},{{{for}\quad k} \geq 1.}$

Finally one obtains an equation of the kind:

α₀ =f(α₁, α₂ . . . , α_(s−1))  (24)

where f is a polynomial of the first degree in variables α₁, α₂ . . . ,α_(s−1).

The quantity to be minimized is a polynomial of degree 2 in variablesα₀, α₁, α₂ . . . , α_(s−1) which has for an equation: $\begin{matrix}{{w(0)} - {\alpha\varphi} + {\sum\limits_{k = 0}^{s - 1}{\sum\limits_{j = 0}^{s - 1}{\alpha_{k}\alpha_{j}{v( {j + k + 1} )}}}} + {( {1 - \alpha} ){\sum\limits_{k = 0}^{s - 1}{\sum\limits_{j = 0}^{s - 1}{\alpha_{k}\alpha_{j}{v( {j + k} )}}}}} - {2{\sum\limits_{k = 0}^{s - 1}{\alpha_{k}{v(k)}}}} + {2\alpha {\sum\limits_{k = 0}^{s}{\alpha_{k}{w(k)}}}}} & (25)\end{matrix}$

where$\varphi = {\int_{\alpha - 1}^{+ \infty}{\frac{\exp ( {{- \gamma}\quad x} )}{( {1 + x} )^{2}}{x}}}$

which works out numerically $\begin{matrix}{{{w(k)} = {\sum\limits_{n = 0}^{k - 1}{( {- 1} )^{n - k + 1}{v(n)}}}},{{{whenever}\quad k} \neq 0},} & (26)\end{matrix}$

and,

w(0)=ξ  (27)

or better, with the following recursion formula:

w(k)=v(k−1)−w(k−1), for k≧1.  (28)

The minimization looked for, by the deletion of the first derivatives of(25) according to each of the variables α₀, α₁, α₂ . . . , α_(s−1),supplies s equations with s variables: $\begin{matrix}{\sum\limits_{j = 0}^{s - 1}{\alpha_{j}\lbrack {{{v( {u + j + 1} )} + {( {1 - \alpha} ){v( {u + j} )}}} = {{v(u)} - {w(u)}}} }} & (29)\end{matrix}$

for u within the interval 0, s−1.

In these equations, the first (for u=0) is redundant with (27).

With s equations with s unknowns α₀, α₁, α₂ . . . , α_(s−), one findsthat one can solve them in a numerical way, which gives s coefficientsα_(i).

Then the coefficients β_(i) that are being looked for can be obtainedeasily through equations (14) and (15) that have already been shown.

By way of an example, we may consider a circuit with two stages (s=2)with one correlation stage and one interference suppression stage and wewill take the case of there being five perfectly synchronous users (K=5)using pseudo-random sequences each with 63 chips. One then has

σ² _(λ)≈0.06

α≈0.75

γ≈6.66

ξ≈0.91

Φ≈1.06

One is looking for a pair of coefficients (α₀, α₁) such that:$\begin{matrix}{{\int_{\alpha - 1}^{+ \infty}{( {\frac{1}{1 + x} - \alpha_{0} - {\alpha_{1}x}} )( {x + 1 - \alpha} ){\exp ( {{- \gamma}\quad x} )}{x}}} = 0} & (30)\end{matrix}$

and such that: $\begin{matrix}{{\int_{\alpha - 1}^{+ \infty}{( {\frac{1}{1 + x} - \alpha_{0} - {\alpha_{1}x}} )^{2}( {x + 1 - \alpha} ){\exp ( {{- \gamma}\quad x} )}{x}}}{{be}\quad a\quad {minimum}}} & (31)\end{matrix}$

Equation (30) gives us $\begin{matrix}{{\alpha_{0}( \frac{1}{\gamma^{2}} )} = ( {\frac{1}{\gamma} - {{\alpha\xi exp}( {\gamma ( {\alpha - 1} )} )}} )} & (32)\end{matrix}$

or:

α₀≈1.02

By deriving expression (31) with respect to α₁, one obtains:$\begin{matrix}{{\alpha_{1}\lbrack {\frac{{\gamma^{3}( {\alpha - 1} )}^{3} + {3{\gamma^{2}( {\alpha - 1} )}^{2}} + {6{\gamma ( {\alpha - 1} )}} + 6}{\gamma^{3}} + {( {1 - \alpha} )\frac{{\gamma^{3}( {\alpha - 1} )}^{2} + {2( {1 + {\gamma ( {\alpha - 1} )}} )}}{\gamma^{3}}}} \rbrack}{{\exp ( {- {\gamma ( {\alpha - 1} )}} )} = {{{\exp ( {- {\gamma ( {x - 1} )}} )}\lbrack {\frac{{\gamma ( {\alpha - 1} )} + 1}{\gamma^{3}} - \frac{\alpha}{\gamma}} \rbrack} + {\alpha\xi}}}} & (33)\end{matrix}$

or

α₁≈0.78

which gives us

β₁=−α₁≈0.78

β₀=−β₁+α₀0.24

This example, which involves two coefficients corresponds therefore to alinear approximation α₀λ⁰+α₁λ¹, i.e. 1.02−0.78λ, deemed to at best, comeclose to 1/1 +λ.

The following tables correspond to various situations in which a numberof stages s ranges from 1 to 5 and a number of users K ranges from 2 to10. These tables give directly the weighting coefficients β of theoutputs of s stages (for s=2 and K=5, one may refer to the previousexample).

TABLE 1 s = 2 β_(i) K = 2 K = 3 K = 4 K = 5 K = 6 K = 7 K = 8 K = 9 K =10 β₀ 0.14 0.19 0.22 0.24 0.25 0.27 0.28 0.30 0.30 β₁ 0.85 0.82 0.800.78 0.77 0.76 0.76 0.75 0.75

TABLE 2 s = 3 β_(i) K = 2 K = 3 K = 4 K = 5 K = 6 K = 7 K = 8 K = 9 K =10 β₀ 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.01 0.01 β₁ 0.32 0.40 0.430.46 0.49 0.51 0.53 0.55 0.56 β₂ 0.66 0.60 0.55 0.52 0.50 0.48 0.47 0.460.45

TABLE 3 s = 4 β_(i) K = 2 K = 3 K = 4 K = 5 K = 6 K = 7 K = 8 K = 9 K =10 β₀ 0.00 0.00 −0.01 −0.02 −0.02 −0.03 −0.04 −0.04 −0.05 β₁ 0.14 0.12  0.15   0.17   0.19   0.21   0.23   0.24   0.26 β₂ 0.49 0.50   0.52  0.54   0.55   0.56   0.56   0.57   0.58 β₃ 0.37 0.39   0.34   0.30  0.28   0.26   0.25   0.23   0.22

TABLE 4 s = 5 β_(i) K = 2 K = 3 K = 4 K = 5 K = 6 K = 7 K = 8 K = 9 K =10 β₀   0.00 0.00 −0.01 −0.01 −0.02 −0.02 −0.03 −0.04 −0.05 β₁   0.360.02   0.03   0.04   0.04   0.05   0.05   0.06   0.06 β₂   1.34 0.27  0.31   0.35   0.38   0.40   0.42   0.44   0.46 β₃   0.37 0.48   0.47  0.46   0.45   0.44   0.43   0.43   0.22 β₄ −1.08 0.22   0.18   0.16  0.14   0.13   0.11   0.10   0.10

TABLE 5 s = 6 β_(i) K = 2 K = 3 K = 4 K = 5 K = 6 K = 7 K = 8 K = 9 K =10 β₀ −0.09 0.00 0.00 0.00 −0.01 −0.01 −0.02 −0.02 −0.03 β₁ 1.24 0.000.00 0.00 −0.01 −0.09 −0.01 −0.02 −0.02 β₂ 9.83 0.16 0.15 0.18 0.20 0.20.24 0.26 0.28 β₃ 11.78 0.4 0.41 0.43 0.45 0.53 0.47 0.48 0.48 β₄ −8.890.3 0.35 0.32 0.30 0.32 0.27 0.26 0.24 β₅ −12.57 0.09 0.09 0.07 0.060.05 0.05 0.04 0.04

FIGS. 4, 5 and 6 allow one to compare the theoretical performance of areceiver conforming to the invention with that of known receivers.

In FIG. 4, firstly the bit error rate (TEB) is shown as a function ofthe ratio (K−1)/M where K is the number of users and M is the processinggain. In the case illustrated M is equal to 63 (number of chips perbit).

The bit error rate increases with the number of users and reduces whenthe processing gain increases. The curve 20 corresponds to a traditionalreceiver without any interference suppression stages; curve 22 to areceiver with one suppression stage; curve 24 to a receiver with twosuppression stages and curve 25 to a receiver according to the inventionwith one suppression stage and the linear weighting described. Theperformance is better than with an equal number of interference stages(in this case 1) and as good as that with two stages as soon as (K−1)/Mis greater than 0.06, i.e. with five or more users.

FIGS. 5 and 6 are simulations representing the bit error rate (TEB) as afunction of the signal to noise ratio RSB. The error rate becomessmaller as the signal to noise ratio increases. In FIG. 5, the curve 30corresponds to a traditional receiver without any interferencesuppression stages; curve 32 corresponds to a receiver with one parallelinterference suppression stage; curve 34 corresponds to a receiver withtwo parallel interference suppression stages curve 36 corresponds to areceiver conforming to patent U.S. Pat. No. 5,553,062 (with weightingcoefficients 1/2^(i)) curve 38 corresponds to a receiver that conformsto the article by S. MOSHAVI at al. already mentioned (quadraticweighting); curve 40 corresponds to a receiver that conforms to thisinvention; finally curve 42 corresponds to the theoretical case of areceiver with perfect decorrelation.

This simulation corresponds to a DQPSK type modulation (“DifferentialQuaternary Phase Shift Keying” or differential phase modulation withfour states). It also corresponds to the case where the impulse responseis formed from a single spectral line, in a theoretical channel wherethere would be only one path. The noise is assumed to be Gaussian,white, centered and additive.

FIG. 6 corresponds to the same assumptions (DQPSK modulation andcentered additive Gaussian white noise) but also assumes that inaddition to the main path, there are three supplementary paths inaccordance with RAYLEIGH's law. The curves are marked as for FIG. 5 witha difference of 20 in the reference numbers: 50 traditional receiverwithout any interference suppression; 52: receiver with one interferencesuppression stage; 54: receiver with two interference suppressionstages; 56: receiver according to U.S. Pat. No. 5,553,062; 58: receiveraccording to S. MOSHAVI et al.; 60: receiver according to the invention;62: theoretical receiver.

These results clearly show the improvement provided by the invention,since the bit error rate is the lowest.

FIG. 7 illustrates a receiver according to the invention for theparticular case of five users and three stages. One can see on thisFigure, a first stage EO with five parallel channels C₁, C₂, C₃, C₄, C₅(K=5), each channel being allocated to a particular pseudo-randomsequence and being capable of supplying a first estimate Z₀ of the datareceived and two interference suppression stages E₁, E₂ with five inputsand five outputs, three weighting means (WGT) M₀, M₁, M₂ multiplying theoutputs Z₀, Z₁, Z₂ by the coefficients β₀, β₁, β₂ equal respectively to0.02, 0.46 and 0.52, an adder ADD summing the outputs from the weightingmeans, and a decision making means D linked to the adder ADD andsupplying the data d1, d2, d3, d4 and d5.

FIG. 8 is a flow chart illustrating the general algorithm for obtainingthe coefficients β. It comprises the following operations:

201: determination of σ_(λ) by simulations

202: determination of the value of γ via expression (17),

203: determination of the distribution p (λ),

204: calculation of the coefficients α₀, . . . , α_(s−1) via (29)

205: calculation of the coefficients β₀, . . . , β_(s−1) via (14) and(15)

FIG. 9 is a flow chart illustrating the particular algorithmcorresponding to the particular case of FIG. 7. The operations are thefollowing:

300: one specifies that the communications are synchronous

301: determination that σ² _(λ)=0.06

302: determination that γ=6.66 and a =0.75,

303: calculation of p(λ): p (λ)=44.35 (λ+0.25) exp (−6.66λ−4.99)

304: determination that α₀=1

α₁=−0.98

α₂=0.52

305: determination that β₀=0.02

β₁=0.46

β₂=0.52

What is claimed is:
 1. A receiver for Code Division Multiple Access(CDMA) transmission, this transmission being accessible to a pluralityof K users each transmitting a message made up of a plurality of Nbinary data, each piece of data pertinent to a user being transmittedafter spectrum spreading by a pseudo-random binary sequence belonging tothat user, this receiver comprising s stages in series, of which: afirst stage of reception of a global signal corresponding to all thesignals transmitted by the K users, this first stage comprising Kchannels in parallel, each channel being allocated a particularpseudo-random sequence and being capable of supplying a first estimateof the data received corresponding to the user having used thatpseudo-random sequence, this first stage thereby supplying K signals onK outputs, (s−1) stages of multiple access interference suppression,each of these stages having K inputs and K outputs, the K inputs of thefirst interference suppression stage being connected to the K outputs ofthe first reception stage, and the K inputs of the other interferencesuppression stages being connected to the K outputs from theinterference suppression stage that precedes it, means of weighting eachgroup of K signals supplied through the K outputs from each of the sstages, the output signals from a stage of rank i (i being between 0 ands−1) being weighted by a coefficient β_(i) the coefficients β_(i) beingchosen so that a certain quantity is a minimum, an adder with s groupsof K inputs to receive the s groups of K weighted signals, a decisionmaking means, connected to the adder and receiving, for each user, aweighted sum of signals and supplying the corresponding data finallytransmitted, this receiver being characterized by the choice of theweighting coefficients β_(i) in the following way: A being a matrix ofNK lines and NK columns in which the elements of the main diagonal arezeros and the elements outside the diagonal reflect theintercorrelations between the signals transmitted by the K users for theN different binary data of the transmitted messages, this matrix Ahaving NK pertinent values λ_(j) distributed in accordance with acertain distribution p(λ), the polynomial expansion α₀λ⁰ _(j)+α₁λ¹_(j)+. . . +α_(i)λ^(i) _(j)+. . . +α_(s−1)λ_(j) ^(s−1), where the α_(i)are coefficients, having with the quantity 1/(1+λ_(j)), a deviationdesignated e(λ_(j)) for each pertinent value λ_(j), the quantity that ismade a minimum is the sum, for all pertinent values λ_(j) of the squareof this deviation, weighted by the distribution of the pertinent values,i.e.${\sum\limits_{j = 0}^{{NK} - 1}\quad {p\quad {(\lambda)\lbrack {e( \lambda_{j} )} \rbrack}^{2}}},$

with in addition the condition${{\sum\limits_{j = 0}^{{NK} - 1}{{p( \lambda_{j} )}{e( \lambda_{j} )}}} = 0},$

this double constraint defining the coefficients α_(i), the weightingcoefficients β_(I) modifying each stage of the receiver are derived fromcoefficients α_(I) by the equations β_(i)=(−1)^(i)(α_(i)+α_(i+1)) forvalues of i going from 0 to s−2 and β_(i)=(−1)^(i)α_(i) for i=s−1.
 2. Areceiver according to claim 1, in which one takes for distribution p(λ)of the pertinent values of the matrix A, an approximate expression equalto γ²(λ+1−a)exp[−γ(λ+1−a)] where γ and a are suitable constants.
 3. Areceiver according to claim 2 for synchronous communications, comprisingtwo stages (s=2), a first reception stage and an interferencesuppression stage, in which: the weighting coefficient β_(0 is) betweenabout 0.14 and about 0.30, the second weighting coefficient β₁ isbetween about 0.85 and about 0.75.
 4. A receiver according to claim 1for synchronous communications, comprising three steps (s=3), a firstreception stage followed by two interference suppression stages, inwhich: the first weighting coefficient β₀ is between about 0.01 andabout 0.02, the second weighting coefficient β₁ is between about 0.32and about 0.56, the third weighting coefficient β₂ is between about 0.66and about 0.45.
 5. A receiver according to claim 1 for synchronouscommunications, comprising four stages (s=4), a reception stage followedby three interference suppression stages, in which: the first weightingcoefficient β₀ is approximately zero, the second weighting coefficientβ₁ is between about 0.14 and about 0.26, the third weighting coefficientβ₂ is between about 0.49 and about 0.58, the fourth weightingcoefficient β₃ is between about 0.37 and about 0.22.
 6. A receiveraccording to claim 1 for synchronous communications, comprising fivestages (s=5), a reception stage followed by four interferencesuppression stages, in which: the weighting coefficient β₀ isapproximately zero, the weighting coefficient β₁ is close to 0.36 fortwo users or between about 0.02 and about 0.06 for more than two users,the weighting coefficient β₂ is close to 1.34 for two users or betweenabout 0.27 and about 0.46 for more than two users, the weightingcoefficient β₃ is close to 0.37 for two users or between about 0.48 andabout 0.42 for more than two users, the weighting coefficient β₄ isclose to −1.08 for two users or between about 0.22 and about 0.10 formore than two users.
 7. A receiver according to claim 1 for synchronouscommunications, comprising six stages (s=6), a reception stage followedby five interference suppression stages, in which: the weightingcoefficient β₀ is approximately zero, the weighting coefficient β₁ isclose to 1.24 for two users or approximately zero for more than twousers, the weighting coefficient β₂ is close to 9.83 for two users orbetween about 0.16 and about 0.28 for more than two users, the weightingcoefficient β₃ is close to 11.78 for two users or between about 0.40 and0.48 for more than two users, the weighting coefficient β₄ is close to−8.89 for two users or between about 0.3 and 0.24 for more than twousers, the weighting coefficient β₅ is close to −12.57 for two users orbetween 0.09 and 0.04 for more than two users.